How do you find the slope given $x + 2 y = 3$ $x + 2y=3$ ?

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Answer 1 · 2017-01-14T19:49:10

Convert the equation to the slope-intercept form - see entire explanation below:

To find the slope we need to convert the equation to the slope-intercept form by solving for $y$ $y$ :

The slope-intercept form of a linear equation is:

$y = m x + b$ $y = color(red)(m)x + color(blue)(b)$

Where $m$ $color(red)(m)$ is the slope and $b$ $color(blue)(b$ is the y-intercept value.

$x + 2 y = 3$ $x + 2y = 3$

$x + 2 y - x = - x + 3$ $x + 2y - color(red)(x) = - color(red)(x) + 3$

$x - x + 2 y = - x + 3$ $x - color(red)(x) + 2y = - color(red)(x) + 3$

$0 + 2 y = - x + 3$ $0 + 2y = -x + 3$

$2 y = - x + 3$ $2y = -x + 3$

$\frac{2 y}{2} = \frac{- x + 3}{2}$ $(2y)/color(red)(2) = (-x + 3)/color(red)(2)$

$(color(red)(cancel(color(black)(2)))y)/cancel(color(red)(2)) = -x/2 + 3/2$

$y = -1/2x + 3/2$

With the equation now in slope intercept form we can see the slope is $color(red)(m = -1/2)$

How do you find the slope given x + 2y=3x+2y=3x + 2y=3?